scholarly journals Almost Sure Convergence of Quadratic Forms in Independent Random Variable

1968 ◽  
Vol 39 (5) ◽  
pp. 1502-1506 ◽  
Author(s):  
Dale E. Varberg
Keyword(s):  
Independent Random Variable ◽  
Quadratic Forms ◽  
Almost Sure Convergence ◽  
Random Variable

scholarly journals Theoretical basis and significance of the variance of discharge as a bidimensional variable for the design of lateral lines of micro-irrigation

2009 ◽  
Vol 66 (4) ◽  
pp. 563-569
Author(s):  
Euro Roberto Detomini ◽  
Brendan Power ◽  
José Antônio Frizzone
Keyword(s):  
Independent Random Variable ◽  
Theoretical Basis ◽  
Systems Design ◽  
Statistical Design ◽  
Random Variable ◽  
Point Of View ◽  
Soil Slope ◽  
Irrigation Systems ◽  
Lateral Lines ◽  
Micro Irrigation

In order to support the theoretical basis and contribute to the improvement of educational capability issues relating to irrigation systems design, this point of view presents an alternative deduction of the variance of the discharge as a bidimensional and independent random variable. Then a subsequent brief application of an existing model is applied for statistical design of laterals in micro-irrigation. The better manufacturing precision of emitters allows lengthening a lateral for a given soil slope, although this does not necessarily mean that the statistical uniformity throughout the lateral will be more homogenous.

Convergence rates in the law of large numbers. II

1968 ◽  
Vol 64 (2) ◽  
pp. 485-488 ◽  
Author(s):  
V. K. Rohatgi
Keyword(s):  
Convergence Rates ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Random Variable ◽  
Rates Of Convergence ◽  
Independent Random Variables ◽  
Large Numbers ◽  
Present Context ◽  
Image Position ◽  
Uniformly Bounded

Let {Xn: n ≥ 1} be a sequence of independent random variables and write Suppose that the random vairables Xn are uniformly bounded by a random variable X in the sense thatSet qn(x) = Pr(|Xn| > x) and q(x) = Pr(|Xn| > x). If qn ≤ q and E|X|r < ∞ with 0 < r < 2 then we have (see Loève(4), 242)where ak = 0, if 0 < r < 1, and = EXk if 1 ≤ r < 2 and ‘a.s.’ stands for almost sure convergence. the purpose of this paper is to study the rates of convergence ofto zero for arbitrary ε > 0. We shall extend to the present context, results of (3) where the case of identically distributed random variables was treated. The techniques used here are strongly related to those of (3).

scholarly journals Strong laws of large numbers for arrays of rowwise independent random elements

1987 ◽  
Vol 10 (4) ◽  
pp. 805-814 ◽  
Author(s):  
Robert Lee Taylor ◽  
Tien-Chung Hu
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Complete Convergence ◽  
Almost Sure Convergence ◽  
Random Variable ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Rowwise Independent ◽  
Uniformly Bounded

Let{Xnk}be an array of rowwise independent random elements in a separable Banach space of typep+δwithEXnk=0for allk,n. The complete convergence (and hence almost sure convergence) ofn−1/p∑k=1nXnk to 0,1≤p<2, is obtained when{Xnk}are uniformly bounded by a random variableXwithE|X|2p<∞. When the array{Xnk}consists of i.i.d, random elements, then it is shown thatn−1/p∑k=1nXnkconverges completely to0if and only ifE‖X11‖2p<∞.

scholarly journals Rate of the Almost Sure Convergence of a Generalized Regression Estimate Based on Truncated and Functional Data

2020 ◽  
pp. 480-491
Author(s):  
Halima Boudada ◽  
Sara Leulmi ◽  
Soumia Kharfouch
Keyword(s):  
Functional Data ◽  
Dimensional Space ◽  
Almost Sure Convergence ◽  
Regression Function ◽  
Random Variable ◽  
Infinite Dimensional Space ◽  
Left Truncation ◽  
Regression Estimate ◽  
Infinite Dimensional ◽  
Generalized Regression

In this paper, a nonparametric estimation of a generalized regression function is proposed. The real response random variable (r.v.) is subject to left-truncation by another r.v. while the covariate takes its values in an infinite dimensional space. Under standard assumptions, the pointwise and the uniform almost sure convergences, of the proposed estimator, are established

scholarly journals On the Spectra of General Random Graphs

10.37236/702 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Fan Chung ◽  
Mary Radcliffe
Keyword(s):  
Independent Random Variable ◽  
Random Graph ◽  
Random Graphs ◽  
Power Law ◽  
Error Bounds ◽  
Adjacency Matrix ◽  
Random Variable ◽  
Degree Sequences ◽  
Chernoff Inequality

We consider random graphs such that each edge is determined by an independent random variable, where the probability of each edge is not assumed to be equal. We use a Chernoff inequality for matrices to show that the eigenvalues of the adjacency matrix and the normalized Laplacian of such a random graph can be approximated by those of the weighted expectation graph, with error bounds dependent upon the minimum and maximum expected degrees. In particular, we use these results to bound the spectra of random graphs with given expected degree sequences, including random power law graphs. Moreover, we prove a similar result giving concentration of the spectrum of a matrix martingale on its expectation.

scholarly journals Valuation of Cliquet-Style Guarantees with Death Benefits in Jump Diffusion Models

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2011
Author(s):  
Yaodi Yong ◽  
Hailiang Yang
Keyword(s):  
Independent Random Variable ◽  
Linear Combination ◽  
Random Variable ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Financial Asset ◽  
Exponential Distributions ◽  
Inverse Transform ◽  
Insurance Product

This paper aims to value the cliquet-style equity-linked insurance product with death benefits. Whether the insured dies before the contract maturity or not, a benefit payment to the beneficiary is due. The premium is invested in a financial asset, whose dynamics are assumed to follow an exponential jump diffusion. In addition, the remaining lifetime of an insured is modelled by an independent random variable whose distribution can be approximated by a linear combination of exponential distributions. We found that the valuation problem reduced to calculating certain discounted expectations. The Laplace inverse transform and techniques from existing literature were implemented to obtain analytical valuation formulae.

scholarly journals Almost sure convergence of quadratic forms in random variables

1973 ◽  
Vol 15 (3) ◽  
pp. 257-258
Author(s):  
V. K. Rohatgi
Keyword(s):  
Quadratic Forms ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Real Numbers ◽  
Image Position

Let X1, X2, … be a sequence of random variables and let {ajk}, j,k = 1, 2, …, be a matrix of real numbers. Write We establish the following result.

On the asymptotic properties of a supercritical bisexual branching process

1986 ◽  
Vol 23 (03) ◽  
pp. 820-826 ◽  
Author(s):  
J. H. Bagley
Keyword(s):  
Population Size ◽  
General Class ◽  
Population Model ◽  
Branching Process ◽  
Asymptotic Properties ◽  
Almost Sure Convergence ◽  
Random Variable ◽  
Convergence Result ◽  
Bisexual Population

An almost sure convergence result for the normed population size of a bisexual population model is proved. Properties of the limit random variable are deduced. The derivation of similar results for a general class of such processes is discussed.

Stochastic flowshop no-wait scheduling

1985 ◽  
Vol 22 (1) ◽  
pp. 240-246 ◽  
Author(s):  
E. Frostig ◽  
I. Adiri
Keyword(s):  
Independent Random Variable ◽  
Processing Time ◽  
Random Variables ◽  
Random Variable ◽  
Schedule Length ◽  
Special Cases ◽  
No Wait ◽  
Completion Times ◽  
Sum Of Completion Times

This paper deals with special cases of stochastic flowshop, no-wait, scheduling. n jobs have to be processed by m machines . The processing time of job Ji on machine Mj is an independent random variable Ti. It is possible to sequence the jobs so that , . At time 0 the realizations of the random variables Ti, (i are known. For m (m ≧ 2) machines it is proved that a special SEPT–LEPT sequence minimizes the expected schedule length; for two (m = 2) machines it is proved that the SEPT sequence minimizes the expected sum of completion times.

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